KUWAIT CITY (CNN) --Kuwaiti officials said Thursday a Kuwaiti police sergeant pulled two U.S. soldiers in a civilian vehicle off the road Thursday morning, and then shot them at close range.

The soldiers, who were shot in the face and in the shoulder, are in serious but stable condition.

The soldiers -- who were wearing civilian clothing -- did not return fire. After the two soldiers were shot, the attacker returned home, got some money, and fled across the border to Saudi Arabia, Pentagon sources told CNN. Kuwaiti and Saudi officials are working to bring the man back to Kuwait.

Sources told CNN it's still unclear whether the incident was an individual act or linked to terrorism.

The shooting took place around 10:30 a.m. (2:30 a.m. EST) as the U.S. soldiers were traveling between Camp Doha -- a U.S. military base -- and Oraifijan, a U.S. military spokesman said.

Their injuries are not considered life-threatening, the spokesman said, adding that they were able to drive themselves to Oraifijan, where they were flown by military aircraft to a military hospital in Kuwait City.

Apparently U.S. soldiers in the area do not wear military uniforms when they are traveling off-base in order to maintain a low profile, the spokesman said.

Their names are not being released, U.S. military sources said. U.S. and Kuwaiti authorities are investigating the shooting.

There are currently about 10,000 U.S. troops in Kuwait, according to the Pentagon. Troops are in Kuwait conducting regularly scheduled military exercises dubbed Operation Desert Spring at a time when the U.S. has been threatening military action against nearby Iraq if they fail to abide by post-Persian Gulf War resolutions calling on them to destroy any weapons of mass destruction. Baghdad has repeatedly said it does not possess such weapons.

The shooting is the latest in a string of violent attacks and threats against U.S. soldiers stationed in Kuwait and comes on the same day as a U.S. missionary was shot and killed in Lebanon. (Full story)

On October 8, two Kuwaiti gunmen suspected of having ties to Osama bin Laden's al Qaeda terrorist network carried out an attack against U.S. troops on Failaka Island, killing one Marine and injuring another.

U.S. military police chased down the two assailants, who were dressed in civilian clothes and driving a pickup, and shot them dead, according to U.S. officials.

The day of the attack a taped message surfaced purporting to be from bin Laden's No. 2 man, Ayman al-Zawahiri, vowing new attacks on Americans. On November 12, the Qatar-based, Arabic language TV network Al-Jazeera broadcast an audiotape later identified to be the voice of bin Laden referring to the killing of a U.S. Marine in Kuwait.

Following the October attack, there were two more shootings involving U.S. troops in Kuwait, but no one was injured.